3 - PROCESS TERMS

Summary

We now introduce a second view of concurrent processes whereby each process is a term over a certain signature of operator symbols. By interpreting these symbols on nets, we will solve the problem of compositionality. As interpretations we take a selection of the operators suggested in Lauer's COSY, Milner's CCS and Hoare's CSP.

Lauer's COSY (Concurrent Systems) is one of the first approaches to compositionality of processes on a schematic, uninterpreted level [LTS79]. It originates from path expressions [CH74] and can thus be seen as an extension of regular expressions to include parallelism. We use here COSY's operator for parallel composition because, as we shall see later in Chapter 4, it enjoys pleasant logical properties.

A significant step beyond COSY is Milner's CCS (Calculus of Communicating Systems) with its conceptual roots in algebra and the λ-calculus [Mil80, Mil83]. From CCS we take the idea that processes are recursive terms over certain operator symbols, i.e. they form the smallest set that is generated by the operator symbols and closed under parameterless recursion. In COSY only iteration is present as might be clear from its background in regular expressions. By using recursion we ensure that process terms are Turing powerful even on the schematic level without the help of interpreted values or variables. We also take CCS's choice operator because it allows a very clear treatment on the level of nets, and its notion of action morphism by which actions can be renamed.